Lecture 8 (part 2)

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Unformatted text preview: than di will occur in a standard normal distribution. X = exercise price e = 2.7183 r = risk­free interest rate t = time until the option expires (option period) ln (P/X) = natural logarithm of P/X σ2 = variance of rate of return on the stock variance of rate of return on the stock Value of an Option Value of an Option So far, we have assumed European options, which can only be exercised on expiry. What about American options? What is their option value? Example: Consider an American call option with exercise price of \$50 exercisable at any time prior to maturity during next 2 months. Current stock price is \$55 & will not pay dividends during the option period. Call price is \$7. Value of an Option Value of an Option Value of an option Option value before expiry \$7 Option value at expiry Time value = \$2 \$5 Intrinsic value = \$5 X=\$50 \$55 Stock price Value of an Option Value of an Option Option value = Intrinsic value + Time value = (\$55 ­ \$50) + \$2 = \$7 Question: Assume you own the call option & want to own the stock. Should you exercise your call today (before expiry) to buy stock? Value of an Option Value of an Option No!! If you exercise today, payment under call option= \$50. Alternatively, you should sell the call option for \$7 and use the proceeds to buy the stock in market. Payment = \$55 ­ \$7 = \$48 Value of an...
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